satisfiability problem

Given a Boolean expression E, decide if there is some
assignment to the variables in E such that E is true.

A Boolean expression is composed of Boolean variables,
(logical) negation (NOT), (logical) conjunction (AND) and
parentheses for grouping. The satisfiability problem was the
first problem to be proved to be NP-complete (by Cook).

["Introduction to Automata Theory, Languages, and Computation"
by Hopcroft and Ullman, pub. Addison-Wesley].